This chapter focuses on the development and application of simplified climate system models (C3IAM/Climate) and climate impact models (C3IAM/Loss) within Integrated Assessment Models (IAMs). To address the high computational costs of complex Earth system models, C3IAM/Climate employs parameterization methods to streamline carbon cycle processes and climate simulations, efficiently linking greenhouse gas emissions to concentrations, radiative forcing, and global temperature changes. It supports simulations of both global mean temperature and grid-scale temperature responses. C3IAM/Loss integrates climate and socio-economic systems to quantify impacts on macroeconomics, agriculture, human health, and extreme events. The models combine carbon cycle modules (capturing atmosphere-ocean-terrestrial interactions) with climate modules, utilizing statistical and physical approaches to address uncertainties such as climate sensitivity and aerosol forcing. By balancing computational efficiency and accuracy, the study highlights the role of simplified models in regional climate policy analysis and multi-scenario assessments, providing tools to reconcile mitigation costs with climate damage in economic decision-making.